Selective Inference for Time-Varying Effect Moderation

TL;DR

This paper introduces a two-step selective inference method for analyzing how causal effects vary over time with multiple potential moderators, improving interpretability and accuracy in high-dimensional settings.

Contribution

It proposes a novel Gaussian randomization-based approach for valid inference on time-varying effect moderation, addressing limitations of existing methods.

Findings

Achieves valid coverage rates in simulations and real data

Produces shorter, bounded confidence intervals

Outperforms existing methods in accuracy and interpretability

Abstract

Causal effect moderation investigates how the effect of interventions (or treatments) on outcome variables changes based on observed characteristics of individuals, known as potential effect moderators. With advances in data collection, datasets containing many observed features as potential moderators have become increasingly common. High-dimensional analyses often lack interpretability, with important moderators masked by noise, while low-dimensional, marginal analyses yield many false positives due to strong correlations with true moderators. In this paper, we propose a two-step method for selective inference on time-varying causal effect moderation that addresses the limitations of both high-dimensional and marginal analyses. Our method first selects a relatively smaller, more interpretable model to estimate a linear causal effect moderation using a Gaussian randomization approach. We then condition on the selection event to construct a pivot, enabling uniformly asymptotic semi-parametric inference in the selected model. Through simulations and real data analyses, we show that our method consistently achieves valid coverage rates, even when existing conditional methods and common sample splitting techniques fail. Moreover, our method yields shorter, bounded intervals, unlike existing methods that may produce infinitely long intervals.